What is the volume of a cylinder with a radius of 4 centimeters and a height of 5 centimeters?
Understand the Problem
The question asks to calculate the volume of a cylinder given its radius and height. The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height.
Answer
$80\pi \text{ cm}^3$
Answer for screen readers
$80\pi \text{ cm}^3$
Steps to Solve
- Write down the formula for the volume of a cylinder
The formula for the volume $V$ of a cylinder with radius $r$ and height $h$ is:
$$ V = \pi r^2 h $$
- Plug in the given values for radius and height
We are given that the radius $r = 4$ cm and the height $h = 5$ cm. Substituting these values into the formula:
$$ V = \pi (4)^2 (5) $$
- Calculate the square of the radius
$4^2 = 16$, so the equation becomes:
$$ V = \pi (16) (5) $$
- Multiply the numbers together
Multiply 16 and 5:
$$ V = \pi (80) $$
- Simplify the equation
$$ V = 80\pi $$
Therefore, the volume of the cylinder is $80\pi$ cubic centimeters.
$80\pi \text{ cm}^3$
More Information
The volume of a cylinder is expressed in cubic units because it represents a three-dimensional space. In this case, since the radius and height are given in centimeters, the volume is in cubic centimeters (cm³).
Tips
A common mistake is forgetting to square the radius in the formula. Another mistake could be using the diameter instead of the radius in the formula.
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